Question: I have a bag with only red, blue, and green marbles.  The ratio of red marbles to blue marbles to green marbles is $1:5:3$.  There are 27 green marbles in the bag.  How many marbles are there  in the bag?
Solution: Since the ratio of red to blue to green marbles is $1:5:3$, the ratio of green marbles to the total number of marbles is $3/(1+5+3) = 3/9=1/3$.  Since the green marbles are one-third of the total, and there are 27 green marbles, there must be $3\cdot 27 = \boxed{81}$ total marbles.